The Internet of things (IoT) comprises of wireless sensors and actuators connected via access points to the Internet. Often, the sensing devices are remotely deployed with limited battery power and are equipped with energy harvesting equipment. These devices transmit real-time data to the base station (BS), which is used in applications such as anomaly detection. Under sufficient power availability, wireless transmissions from sensors can be scheduled at regular time intervals to maintain real-time data acquisition. However, once the battery is significantly depleted, the devices enter into power saving mode and need to be more selective in transmitting information to the BS. Transmitting a particular piece of sensed data consumes power while discarding it may result in loss of utility at the BS. The goal is to design an optimal dynamic policy which enables the device to decide whether to transmit or to discard a piece of sensing data particularly under the power saving mode. This will enable the sensor to prolong its operation while causing minimum loss of utility to the application. We develop an analytical framework to capture the utility of the IoT sensor transmissions and leverage dynamic programming based approach to derive an optimal real-time transmission policy that is based on the statistics of information arrival, the likelihood of harvested energy, and designed lifetime of the sensors. Numerical results show that if the statistics of future data valuation are accurately predicted, there is a significant increase in utility obtained at the BS as well as the battery lifetime.